Question: Find the area of the region bounded by the graph of $r = \sec \theta,$ the graph of $r = \csc \theta,$ the $x$-axis, and the $y$-axis.
Explanation: If $r = \sec \theta = \frac{1}{\cos \theta},$ then $x = r \cos \theta = 1.$  Thus, the graph of $r = \sec \theta$ is simply the line $x = 1.$

If $r = \csc \theta = \frac{1}{\sin \theta},$ then $y = r \sin \theta = 1.$  Thus, the graph of $r = \csc \theta$ is simply the line $y = 1.$

[asy]
unitsize(2 cm);

fill((0,0)--(1,0)--(1,1)--(0,1)--cycle,gray(0.7));
draw((-0.3,1)--(1.3,1),red);
draw((1,-0.3)--(1,1.3),red);
draw((-0.3,0)--(1.3,0));
draw((0,-0.3)--(0,1.3));
[/asy]

Hence, the region we are interested in is simply the square with vertices $(0,0),$ $(1,0),$ $(1,1),$ and $(0,1),$ which has area $\boxed{1}.$